The spatio-temporal analysis of infectious diseases

传染病在整个社会都非常重要。麻疹、非典、流感或口蹄疫等疾病的流行可能对公众健康构成直接威胁和/或产生严重的经济影响。为了控制这些疾病，至关重要的是要了解疾病是如何随着时间的推移在地理上传播的，以及是什么因素导致一些人被感染，另一些人不被感染。为此，开发了一类新的数学模型，即传染病的个人水平模型(ILM)。这些模型直观、灵活，并已被证明准确地描述了以前观察到的流行病在空间和时间上的模式。然而，ILM是相对较新的，因此有许多传染病问题还不存在特定的模型。计算密集的技术被用来执行这一过程。然而，如果我们有大量数据，或者我们希望估计的数据中有很多缺失值，这些密集的技术可能需要很长时间才能运行；两者通常都是疾病流行的情况。因此，这项研究的目的是做以下工作：1)扩展ILM，使其能够更准确地对更多传染病进行建模；2)改进统计推断过程，使其更有效；3)将新模型应用于收集的关于各种传染病的数据，以回答有关这些疾病的生物学有趣问题(例如：谁面临最大的疾病风险？或“我们如何最好地控制这种疾病？”)；4)使用计算机模拟和推理，以确定未来应该收集什么样的传染病数据，以最有效地提供有关感染过程的信息；以及5)开发非统计学家可以轻松使用的计算机软件。他们说，这些发展然后可以用来加深我们对传染病的了解，并通过这一点，我们控制它们或减轻不必要的严重后果的能力。

Infectious diseases are of great importance across society. Epidemic outbreaks of diseases such as measles, SARS, influenza or foot-and-mouth disease, can pose direct threats to public health and/or have serious economic effects. In order to control such diseases, it is vital to understand how the disease spreads geographically over time, and what factors lead to some individuals becoming infected, and some not. To this end, a new class of mathematical models,  individual-level models (ILMs) for infectious diseases, has been developed. These models are intuitive, flexible, and have been shown to accurately describe the patterns of previously observed epidemics over space and time. However, ILMs are relatively new and so there are many infectious disease problems for which specific models do not yet exist.    A process known as statistical inference is used to derive a model that best fits the observed data. Computationally intensive techniques are used to carry out this process. However, these intensive techniques can take a long time to run if we have a lot of data, or lots of missing values in the data which we wish to estimate; both are often the case with disease epidemics.    The purpose of this research is therefore to do the following: 1) extend ILMs so they can model more infectious diseases, more accurately; 2) improve the statistical inference process to make it more efficient; 3) apply new models to data collected about various infectious diseases to answer biologically interesting questions about those diseases (e.g. "who are most at risk from the disease?" or "how do we best control this disease?"); 4) use computer simulation and inference to determine what sort of infectious disease data should be collected in the future to provide information most efficiently about the infection process; and 5) develop computer software that non-statisticians can use easily.    These developments can then be used to further our understanding of infectious diseases, and through this, our ability to control them or alleviate unnecessarily severe outcomes.